Six years after the Manhattan District Attorney's Office began an investigation that resulted in Donald Trump becoming the first former president ever convicted of a crime, the case continues to be beset by extraordinary curveballs.

The latest is Monday's landmark Supreme Court decision on presidential immunity that led to Tuesday's decision by the judge in his New York criminal case to postpone Trump's sentencing.

"That wasn't just a curve, that was a 12-6 breaking ball," said Michael Cohen, Trump's ex-attorney who was a key witness in the case against him, referring to a baseball pitch that befuddles hitters when it sharply drops.

The Supreme Court found that former presidents enjoy broad immunity for official acts, and said evidence involving those acts cannot be used in prosecutions over unofficial activity. Soon after the decision was released on Monday, Trump's team sent a letter to New York Justice Juan Merchan asking for permission to file a motion laying out why the verdict in Trump's case should be thrown out.

Merchan granted the request and pushed back Trump's sentencing from July 11 to Sept. 18 to consider the question.

As the case enters a new phase, experts remain skeptical that Trump's 11th-hour effort to overturn his conviction will be successful.

"If he engaged in unlawful conduct before he became president, it doesn't seem to me that his efforts when he was president, to either cover up or address that conduct, will be immunized from criminal liability," said Pace University law professor Bennett Gershman, a former New York prosecutor.

Trump's lawyers indicated in their letter that their motion will focus on evidence introduced at trial that related to social media posts, public statements and witness testimony from his time in office. Much of that evidence pertained to what prosecutors described as a 2018 "pressure campaign" designed to keep Cohen from divulging incriminating information about Trump.

"Michael is a businessman for his own account/lawyer who I have always liked & respected. Most people will flip if the Government lets them out of trouble, even if it means lying or making up stories," Trump wrote in one April 2018 tweet entered into evidence.

Trump was convicted in May of 34 counts of falsification of business records for signing off on an effort to cover up reimbursements for a "hush money" payment to an adult film star as he ran for office in 2016.

CBS News legal analyst Rikki Klieman said the context and timing of that scheme make it unlikely Merchan will reverse the conviction.

"I do not believe that the verdict will be set aside," Klieman said. "What is this case about? It's about conduct before he was president of the United States that was designed to influence the outcome of the 2016 election."

Gary Galperin, a Cardozo Law School professor and former Manhattan prosecutor, said Merchan can conclude that some evidence should not have been shown at trial, and still decline to set aside the verdict.

"If there's enough evidence beyond the 'official acts' to sustain the conviction, then it would be what the courts call 'harmless error,'" Galperin said. "No trial is perfect. And the criminal justice system doesn't anticipate or expect perfection."

If Merchan concludes that enough evidence and testimony related to official acts was introduced during the trial to warrant setting aside the verdict, he would likely point to "the exact pieces of evidence" that violated the Supreme Court's opinion, Klieman said.

Prosecutors would be able to use Merchan's findings as guidance if they decided to seek another trial.

"In the event that it is set aside, I would expect that the government would move to re-try the case, and exclude the evidence Judge Merchan decides could be in violation of the Supreme Court decision," Klieman said.

Cohen said it occurred to him Tuesday night that he might be asked to testify against Trump again in a trial do-over. 

As Trump's former lawyer and fixer, and now scorned vocal critic, Cohen faced four days of painstaking, bruising examination during the trial. Trump's lawyers painted him a serial liar determined to seek revenge against the former president, while building a new celebrity career off that effort.

Would he willingly go through that again?

"As it relates to the question of whether or not I'd testify again, I'll take it under advisement," Cohen said. "I'll let you know when the time comes."

Graham Kates is an investigative reporter covering criminal justice, privacy issues and information security for CBS News Digital. Contact Graham at [email protected] or [email protected]